# Infinitely many hyperbolic Coxeter groups through dimension 19

@article{Allcock2006InfinitelyMH, title={Infinitely many hyperbolic Coxeter groups through dimension 19}, author={Daniel Allcock}, journal={Geometry \& Topology}, year={2006}, volume={10}, pages={737-758} }

We prove the following: there are infinitely many finite-covolume (resp. cocompact) Coxeter groups acting on hyperbolic space H^n for every n < 20 (resp. n < 7). When n=7 or 8, they may be taken to be nonarithmetic. Furthermore, for 1 < n < 20, with the possible exceptions n=16 and 17, the number of essentially distinct Coxeter groups in H^n with noncompact fundamental domain of volume less than or equal to V grows at least exponentially with respect to V. The same result holds for cocompact…

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